Group theoretical approach to the analysis of interferometers

A geometric approach to the analysis of interferometers is presented in which beam splitters and phase shifters are described as performing rotations in an abstract three space on the state vector of the light. This formulation allows one to take full advantage of representation theory for the group SU(2) in analyzing interferometer sensitivity. With these techniques it is easy to show that in conventional interferometry, where light enters only one input port, the phase sensitivity scales as the inverse square root of the number of photons that pass through the interferometer during measurement time. By injecting suitably correlated light into both input ports of an interferometer, a phase sensitivity approaching 1/n can be achieved, where n is the number of photons. Input states that allow this sensitivity can readily be identified using SU(2) representation theory. Methods of generating such states using four-wave mixers or parametric amplifiers are described. By employing the group SU(1,1) this formalism may be extended to describe active interferometers in which the beam splitters are replaced by four-wave mixers or parametric devices. Such interferometers can also achieve a phase sensitivity approaching 1/n. The potential advantages of these interferometers over conventional interferometers will be discussed